Question
In a three-digit number, the digit in the unit place is
five times the digit in the hundred’s place. If the digit in the unit’s place and the ten’s place are interchanged, the new number so formed is 36 more than the original number. If the digit in the hundred’s place is one-third of the digit in the ten’s place. What is the 1/27th of the original number?Solution
Let hundred’s digit = ‘x’ Then unit’s digit = 5x and ten’s digit = 3x ∴ Number = 100x + 30x + 5x = 135x Again, hundred’s digit = x Ten’s digit = 5x and unit’s digit = 3x ∴ Number = 100x + 50x + 3x = 153x According to the question, ⇒ 153x – 135x = 27 ⇒ 18x = 36 ⇒ x = 2 ∴ Original number = 135x = 270 ∴ 1/27th of original number = 270/27 = 10
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